Ask Marian

I do disagree. I think that the purpose of simplifying fractions is to ensure that the student has the best possible sense of the size of the fraction. For example, simplifying a fraction like (frac{18}{36}) to (frac{1}{2}) gives a better sense, immediately, of its size. But I am not convinced that (frac{14}{57}) is any more meaningful than, say, (frac{28}{114}). Neither means that much to us, so why bother simplifying?

In fact, for some people, a fraction that has not been simplified such as (frac{4}{10}) might be even more meaningful than (frac{2}{5}) since we use tenths so frequently.

You might have noticed that I’ve used the word “simplify” rather than “reduce.” This was deliberate since using the term “reduce” might make students think the fraction has gotten smaller, and we want students to realize it is still the same size.

Some of the commercial algebra tile sets are a little better than others at ensuring that the variable tile is not an integer number of tiles long. If students carefully line up their x-tile with 1-tiles, they will see it is not exactly 5.

More importantly, you need to emphasize to students that 3x + 5 is a way of saying “5 more than any triple” and that x doesn’t have a value until you decide what number you are trying to triple. For example, if you were tripling 5, the expression would equal 20 but not if you were tripling 2.

I think sorting is taught in almost every subject area. Every time we use a name for something, we are implicitly sorting. In math, we sort numbers when we call some numbers squares and some not squares or when we call some numbers two-digit numbers and some not. In literacy, we sort writing when we call some things poems and others not, and in music, we sort by genre when we call some music rap and some not. I think we are just making students aware of what they are unconsciously doing all the time.